When photons of wavlength `lambda_(1)` are incident on an isolated sphere suspended by an insulated thread, the corresponding stopping potential is found to be `Delta V.` When photons of wavelength `lambda_(2)` are used, the corresponding stopping potential was thricle of the above value. If light of wavelength `lambda_(3)` is used, the stopping potential for this case would be

Options

A. `(hc)/(e) [(1)/(lambda_(3)) + (1)/(2 lambda_(2)) - (1)/(lambda_(1))]`
B. `(hc)/(e) [(1)/(lambda_(3)) + (1)/(2 lambda_(2)) - (3)/(lambda_(1))]`
C. `(hc)/(e) [(1)/(lambda_(3)) + (1)/( lambda_(2)) - (1)/(lambda_(1))]`
D. `(hc)/(e) [(1)/(lambda_(3)) - (1)/( lambda_(2)) - (1)/(lambda_(1))]`

Answer

B

Explanation

`K E_(lambda_1) = (hc)/(lambda_(1)) - psi = e Delta V`
`K E_(lambda_2) = (hc)/(lambda_(2)) - psi = 2 e Delta V`
`implies 3 ((hc)/(lambda_(1)) - psi) = (hc)/(lambda_(2)) -psi`
`psi = hc ((3)/(2 lambda_(1)) - (1)/(2 lambda_(2)))`
`implies K E_(lambda_3) = (hc)/(lambda_(3)) - hc [(3)/(2 lambda_(1)) - (1)/(2 lambda_(2))]`
` = hc [(1)/(lambda_(3)) + (1)/(2 lambda_(2)) - (3)/(2 lambda_(1))]`
`e Delta V = hc [(1)/(lambda_(3)) + (1)/(2 lambda_(2)) - (3)/(2 lambda_(1))]`
` Delta V = (hc)/(e) [(1)/(lambda_(3)) + (1)/(2 lambda_(2)) - (3)/(lambda_(1))]`